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The Queen of England has n trees growing in a row in her garden. At that, the i-th (1?≤?i?≤?n) tree from the left has height ai meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all i (1?≤?i?<?n), ai?+?1?-?ai?=?k, where k is the number the Queen chose.

Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes?

Input

The first line contains two space-separated integers: n, k (1?≤?n,?k?≤?1000). The second line contains n space-separated integers a1,?a2,?...,?an (1?≤?ai?≤?1000) — the heights of the trees in the row.

Output

In the first line print a single integer p — the minimum number of minutes the gardener needs. In the next p lines print the description of his actions.

If the gardener needs to increase the height of the j-th (1?≤?j?≤?n) tree from the left by x (x?≥?1) meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the j-th (1?≤?j?≤?n) tree from the left by x (x?≥?1) meters, print on the corresponding line "- j x".

If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them.

Sample test(s)

 

Input

4 1

1 2 1 5

Output 2

+ 3 2

- 4 1

Input 4 1

1 2 3 4

Output 0

Source:

 

#include 
   
    #include 
    
     using namespace std;int main(){    freopen("treerow_testcases", "r", stdin);    int caseNum;    cin >> caseNum;    while(caseNum--)    {        int treeNum,tolerance;        cin >> treeNum >> tolerance;        int *tree = new int [treeNum];        for(int i = 0; i < treeNum; i++)        {            cin >> tree[i];        }        //        int minChange = treeNum;        int base = 0;        for(int i = 0; i < treeNum; i++)        {            int changeNum = 0;              // trees to change            int height = tree[i] - i*tolerance; // the first tree's height after changed            if(height <= 0) continue;       // tree's height can't be zero            // chose the i as the base, count the trees need to change            for(int j = 0; j < treeNum; j++)            {                if(height != tree[j])                {                    changeNum++;                }                height += tolerance;            }            if(changeNum == 0)            {                base = i;                minChange = changeNum;                break;            }            else if(changeNum < minChange)            {                base = i;                minChange = changeNum;            }        }        cout << minChange << endl;        int height = tree[base] - base*tolerance;        for(int i = 0; i < treeNum; i++)        {            if(height != tree[i])            {                cout << ((height > tree[i])? "+":"-") << i+1 << " ";                cout << ((height > tree[i])? (height - tree[i]) : (tree[i] - height)) << endl;            }            height += tolerance;        }        //        delete [] tree;    }    return 0;}
    
   

 

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